Given the Production Function Y = a

Given the production function Y = A

and fixed values for the saving rate and depreciation,if productivity is growing at an average rate of three percent,and the labor input grows at two percent,there is a unique growth rate of capital that is sustainable.That is,if the growth rate of capital is either higher or lower than this steady-state value,then it must eventually change,even if nothing else in the economy changes.Calculate this steady-state growth rate of capital,and explain why it alone is a sustainable rate.[Hint: Use the fact that the growth rates of output and capital per worker are 43% higher than the growth rate of productivity.]